# On the Quantification of Image Reconstruction Uncertainty without Training Data

arXiv: https://arxiv.org/abs/2311.09639 · HTML: https://mlsanity.com/paper/2311.09639/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 62 references that are in the map.
- First posted on arXiv 16 Nov 2023.

## Builds on (most cited first, 30 of 35)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs](https://mlsanity.com/paper/1711.11585/) (2017)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam](https://mlsanity.com/paper/1806.04854/) (2018)
- [Robust Learning with Jacobian Regularization](https://mlsanity.com/paper/1908.02729/) (2019)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [Understanding and Mitigating Exploding Inverses in Invertible Neural Networks](https://mlsanity.com/paper/2006.09347/) (2020)
- [SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows](https://mlsanity.com/paper/2007.02731/) (2020)
- [Intermediate Layer Optimization for Inverse Problems using Deep Generative Models](https://mlsanity.com/paper/2102.07364/) (2021)
- [Simulation Intelligence: Towards a New Generation of Scientific Methods](https://mlsanity.com/paper/2112.03235/) (2021)
- [Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging](https://mlsanity.com/paper/2010.14462/) (2020)
- [Reducing Uncertainty in Undersampled MRI Reconstruction with Active Acquisition](https://mlsanity.com/paper/1902.03051/) (2019)
- [Composing Normalizing Flows for Inverse Problems](https://mlsanity.com/paper/2002.11743/) (2020)

## Built on by (most cited first, 1 of 1)

- [Discriminant Distance-Aware Representation on Deterministic Uncertainty Quantification Methods](https://mlsanity.com/paper/2402.12664/) (2024)

## Abstract (arXiv)

Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation of the complete posterior of unrecoverable targets. This, in turn, facilitates a probabilistic interpretation of observational data for decision-making. In this study, we propose a deep variational framework that leverages a deep generative model to learn an approximate posterior distribution to effectively quantify image reconstruction uncertainty without the need for training data. We parameterize the target posterior using a flow-based model and minimize their Kullback-Leibler (KL) divergence to achieve accurate uncertainty estimation. To bolster stability, we introduce a robust flow-based model with bi-directional regularization and enhance expressivity through gradient boosting. Additionally, we incorporate a space-filling design to achieve substantial variance reduction on both latent prior space and target posterior space. We validate our method on several benchmark tasks and two real-world applications, namely fastMRI and black hole image reconstruction. Our results indicate that our method provides reliable and high-quality image reconstruction with robust uncertainty estimation.